Community Detection

1
Community Detection

• Definition Community Detection
• Girwan Newman Approach
• Hierarchical Clustering

2
Community Detection
3
Community Detection Girvan Newman Approach
4
Girwan Newman Approach Modularity
5
Variations of Girwan Newman Algorithm
6
Hierarchical Clustering Algorithms

• Important
• Clustering obtained by cutting the dendo-gram at
  a desired level.
• Each connected component forms a cluster.
• Basically we use some similarity threshold to get
  the clusters of desired quality.

7
Hierarchical Clustering Algorithms
8
Variations of Agglomerative clustering-1
9
Variations of Agglomerative clustering-2
10
Variations of Agglomerative clustering-3
11
Strength Weaknesses

• Strengths of Hierarchical Clustering
• Do not require information regarding number of
  clusters. Any desired number of clusters can be
  obtained by cutting the dendogram at the proper
  level.
• Weaknesses
• Not efficient -- the complexity is O(n2).
• Once a decision is made to combine two clusters,
  it cannot be undone.
• No objective function is directly minimized.

12
Pseudo code Agglomerative Clustering
Source Walter et. al. Fast Agglomerative
Clustering for Rendering
13
Pseudo code
Pseudo code for Agglomerative Clustering, based
on KD-Tree
14
References

• P.-N. Tan, M. Steinbach, and V. Kumar, editors.
  "Introduction to Data Mining." Pearson Addison
  Wesley, 2005.
• B. Walter, K. Bala, M. Kulkarni, and K. Pingali.
  "Fast Agglomerative Clustering for Rendering."
  IEEE Symposium on Interactive Ray Tracing, 2008.
• Girvan M. and Newman M. E. J., Community
  structure in social and biological networks ,
  Proc. Natl. Acad. Sci. USA 99, 78217826 (2002)
• Andrea Lancichinetti and Santo Fortunato (2011).
  "Limits of modularity maximization in community
  detection". Physical Review E 84 066122.
  arXiv1107.1155
• Survey article Communities in Networks (Notices
  of the American Mathematical Society.